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functional analysis - Where can I find the paper Un théorème de . . . J P Aubin, Un théorème de compacité, C R Acad Sc Paris, 256 (1963), pp 5042–5044 It seems this paper is the origin of the "famous" Aubin–Lions lemma This lemma is proved, for example, here and here, but I'd like to read the original work of Aubin However, all I got is only a brief review (from MathSciNet)
modular arithmetic - Prove that that $U (n)$ is an abelian group . . . 1 Let a ∈ Un a ∈ U n then we have to show that there exists b ∈ Un b ∈ U n such that a b a b mod n = 1 n = 1 Let us suppose o(a) = p ap = e o (a) = p a p = e Now if b b is inverse of a a then a b a b mod n = 1 n = 1 holds i e a b = x(n) + 1 a b = x (n) + 1 for some x x (By division algorithm) Now multiply ap−1 a p 1
How to find generators in - Mathematics Stack Exchange For e g- in U(10) = {1, 3, 7, 9} U (10) = {1, 3, 7, 9} are elements and 3 3 7 7 are generators but for a big group like U(50) U (50) do we have to check each and every element to be generator or is there any other method to find the generators?
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Prove that the sequence (1+1 n)^n is convergent [duplicate] It is hard to avoid "the concept of calculus" since limits and convergent sequences are a part of that concept On the other hand, it would help to specify what tools you're happy with using, since this result is used in developing some of them (For example, if you define ex = limn→∞(1 + x n)n e x = lim n → ∞ (1 + x n) n, then clearly we should not be using ex e x in the process of
(Un-)Countable union of open sets - Mathematics Stack Exchange A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
When is the group of units in $\\mathbb{Z}_n$ cyclic? Let Un U n denote the group of units in Zn Z n with multiplication modulo n n It is easy to show that this is a group My question is how to characterize the n n for which it is cyclic Since the multiplicative group of a finite field is cyclic so for all n n prime, it is cyclic However I believe that for certain composite n n it is also cyclic Searching through past posts turned up this
Prove that the order of $U(n)$ is even when $n gt;2$. I'm trying to provide a solution to the following claim: "The order of U(n) U (n) is even when n> 2 n> 2 " Note: here, U(n) U (n) is the set of all positive elements that are less than and relatively prime to n n I think I've correctly proven the claim, but I couldn't find anything similar online So, I would appreciate any criticism corrections regarding my proof (me being fairly new to